During translation, the tRNA molecule carrying the correct amino acid corresponding to its anticodon sequence must base pair with the codon of the mRNA. What would happen in the case where the wrong anticodon successfully binds to a codon

The tRNA would be unable to read the mRNA CODON, and will be unable to carry its corresponding amino acid

Explanation:

Protein synthesis occurs in two major stages; transcription and translation. Transcription involves the synthesis of a mRNA molecule while translation involves reading the sequence of the mRNA in order to synthesize amino acids that forms protein. Let's look at translation in details. Translation occurs with the help of a type of RNA molecule called transfer RNA (tRNA) present in the RIBOSOME (site of protein synthesis).

The tRNA possesses a group of three nucleotides called ANTICODON, which it uses to read the mRNA codon that is complementary to it i.e. an anticodon UAC will read mRNA codon AUG. The tRNA binds to the mRNA molecule in order to assess its nuceleotide sequence. Once, a complementary anticodon succesfully reads a particular mRNA codon, it carries the amino acid encoded by the mRNA codon it reads to the growing polypeptide chain. This is the normal translation process.

However, as stated in the question, that if a wrong anticidon successfully binds to a codon. This means that the anticodon that binds to the mRNA codon is not complementary to it. What would happen in this case is that the Anticodon will be unable to read that particular codon it binds to because the complementary base pairing rule is used to read i.e. A-U, G-C. Once, the anticodon cannot read the mRNA codon, the tRNA will also be unable to carry the amino acid that is encoded by that CODON.